Field of the Invention
The present invention relates to the navigation systems for a mobile vehicle, for example boats and underwater vehicles, and more precisely to the systems allowing to improve the safety of navigation thanks to the determination of a safety zone around a boat.
Description of the Related Art
There exist many methods allowing to determine the position of a boat, among which can be mentioned:                the radio-navigation methods (GPS, LORAN, long acoustic base . . . ). These methods allow to position the boat with respect to a reference network provided that the transmission of the waves between the network and the boat is possible;        the dead reckoning navigation methods, which also include the inertial navigation methods. These methods allow to position the boat based on an initial position by integrating instantaneous speed or acceleration measurements. Accurate over the short term, the dead reckoning navigation tends to become inaccurate over the long term due to the accumulation of the integrated errors of the sensors; and        the terrain navigation methods. These methods consist in using measurements of the environment made by the boat (altimetry, gravimetry, . . . ) and in deducing the position of the mobile vehicle by comparison to a reference map.        
Used jointly with electronic mapping means, for example a system of the ECDIS (Electronic Chart Display Information System) type, these methods allow to represent the estimated position of the boat on a geographic map.
During navigation in waters having obstacles to navigation, and in particular in shallow sea floor, it is not sufficient to have an estimation of position. It is also required to be able to determine a safety zone around the boat in order to take into account the potential errors of the navigation means. The availability of safety zone information allows to trigger alerts when the position of the boat risks to cross a dangerous navigation zone, for example an isobath determined as a function of the minimum water height necessary to the navigation of the boat, the position of the boat and the isobath being shown on the geographic map.
In order to allow a maximum extension of the accessible zones while ensuring the safety of the boat, it is important that the safety zone be determined accurately without the extent thereof be neither underestimated nor overestimated.
When the boat or the submarine is equipped with a sounder allowing to determine the depth of water under the boat, which is generally the case, there exists a traditional navigation method called “flaque de navigation” in the French terminology, and “pool of errors” in the English terminology, which allows to determine such a zone.
The pool-of-errors method is a method that can be implemented graphically and with no calculation, consisting in determining a safety zone about the position of the boat, called pool of errors, based on the sounder information and on the isobaths of the map, then in displacing this zone over time by taking into account the boat speed and the uncertainty thereof due to the current, for example. This method provides the user with easily intelligible information (the safety zone) that correctly take into account the speed uncertainty accumulation and the non-linearity of the problem. In particular, this method allows to determine navigation zones of any shape. Historically used manually on tracing papers, it is today implanted in electronic mapping systems of the ECDIS type.
The pool-of-errors method is based on the hypothesis, fundamentally false, that the probability of presence of the boat in the pool of errors is uniform. Moreover, the use thereof requires, so as not to place the boat in danger, to strongly overestimate the impact of the tidal errors on the sounding points because it is not adapted to a fine taking into account of these errors. These two points, which are the back side of the method simplicity, lead in practice to favour the robustness to the detriment of the accuracy of determination of the safety zone. Hence, the traditional pool-of-errors method leads to widely overestimate the safety zone, which strongly limits the capacities of operation of the boat.
On the other hand, there exist since several years mathematical methods of non-linear filtering allowing to accurately calculate the probability density of presence of a mobile vehicle on a map, by comparing the measurements of a sounder-type instrument with the bathymetry information contained in a geographical data base. The state of the art of these methods may be found for example in the following publications: Fredrik Gustafsson, Particle Filter Theory and Practice with Positioning Applications, 2010, IEEE Aerospace and Electronic Systems Magazine (25), 7, 53-81 and Niclas Bergman, Lennart Ljung and Frederik Gustafsson, “Terrain Navigation using Bayesian Statistics” IEEE Control Systems Magazine, 1999. The patent document US2012/0022784_A1 also describes a Terrain Aided Navigation (TAN) system comprising a non-linear filtering to estimate the conditional probability distribution of a set of measurements.
By construction, these methods calculate in an approached manner the probability density of presence of the mobile vehicle along the map. From the point of view of the presence probability density estimation, they tend towards the optimum solution, provided that a sufficient calculation power is available to faithfully take into account the different parameters of the model of error. In practice, the use of such methods requires making several simplifying hypotheses, but they nevertheless remain far higher than the linear filtering methods.
Given that the presence probability density is an extremely complex indicator and, in particular, it is not an indicator directly intelligible for a human operator, the non-linear filtering methods produce simpler standard indicators. In particular, the standard indicators used correspond to the statistics of order 1 and 2 of the calculated probability distribution, i.e. the least-squares mean and the correspondent covariance (see for example Gustaffson Equations (7a) and (7b)).
These indicators are easily understandable for an operator, all the more that they are identical in their principles to the conventional indicators issued by the linear filtering methods used in most of systems and to which the operators are hence used. Unfortunately, they are very badly adapted to the navigation in zones having dangerous obstacles and the use thereof may lead to significant risks for the safety.
On the one hand, the least-squares mean, which corresponds to the best available estimate of the position, is not, even generally, a point where a non-zero presence probability exists. For example, if the pool-of-errors method and one of the moderns non-linear filtering methods are used jointly, the case will often be one where the estimated position issued by the non-linear filter is not contained in the pool of errors: in such a case, the boat cannot be at the position estimated by the least-squares mean. On the other hand, the position error covariance neither allows to faithfully represent the extent of the navigation uncertainty: its natural representation corresponds to an ellipse, centred on the least-squares-estimated mean, which has been seen as not being pertinent, whereas the navigation uncertainty is generally a zone of far more complex shape (corresponding to the non-linearity of the problem) and hence very different from an ellipse.
Hence among the two types of methods available today: the conventional pool of errors, on the one hand, and the modern non-linear filtering methods, on the other hand, no one allows to respond correctly to the problem of navigation safety in waters having potentially obstacles. The conventional pool-of-errors method provides, as the condition to be correctly implemented, a robust and easily usable estimation of the safety zone. On the other hand, it is widely under optimum, which leads to strongly restrict the field of operations. Moreover, the conventional pool-of-errors method is a graphical method generally implemented on tracing papers that are manually displaced with respect to a sea floor map. As regards the modern non-linear filtering methods, they are able to estimate relatively accurately the whole presence probability density, which in theory corresponds to the whole information required to ensure the navigation jointly with the map of the operation zone. On the other hand, these methods do not propose directly intelligible indicators or else propose indicators, issued by the linear filtering methods such as the least-squares mean and the covariance, the use of which compromise the navigation safety.
The simultaneous use of the conventional pool-of-errors method and the modern non-linear filtering methods neither allows to solve the problem of safety but accumulate the drawbacks of each of the methods, all the more that, as seen hereinabove, these two methods can give contradictory results.
It hence exists a need for a system and a method for determining a navigation safety zone that, while having the robustness and the simplicity of presentation of the conventional pool-of-errors method, are capable of determining accurately this safety zone and taking into account the non-linearity of the problem of determination of the estimated position.
The availability of such a system and such a method would hence allow to ensure the safety of navigation without thereby restricting uselessly the field of operations.